Unai Emerys team travel to Old Trafford on Wednesday on the back of Sundays north London derby victory over Tottenham.
The 4-2 win represented one of Arsenals best performances under Emery and extended the teams unbeaten run to 19 games.
Manchester United are seventh in the table and could only draw 2-2 with Southampton at the weekend.
The Red Devils have made a shocking start to the season but Torreira anticipates a difficult match at Old Trafford on Wednesday.
He said: Today it was a great opportunity [for us in the battle for the top four]. We managed to win this game that was important for us as a team and for the fans.
Now the game against Manchester [United] is coming. It will be against a direct rival because Manchester are behind us in the table.
We have many goals this season. We are playing in several competitions and we are doing it in the best possible way. And the important thing is to continue growing as a team.
Its true [United are eight points behind] but they are still Manchester United, they are still a very strong team who have a great coach.
They are going to play at home, with a lot of fans and we know that all the matches in this championship are different and very difficult.
Pierre-Emerick Aubameyang scored an early penalty for the Gunners but Spurs still led 2-1 at half-time thanks to goals from Eric Dier and Harry Kane.
Aubameyang levelled after half-time, however, before Alexandre Lacazette put the home side back in front.
Torreira rounded off an impressive performance to make it 4-2 before Tottenham were reduced to ten men as Jan Vertonghen was shown a second yellow card.
Speaking after the win, Torreira also lifted the lid on Emerys half-time team talk that inspired the Gunners fine victory.[Emery told us] to be calm, to continue playing because there were 45 more minutes left, that we keep attacking because obviously in the second half we were going to find more spaces, he said.
In fact, it happened and we scored the goals at key moments.
In the first half we started very strong, pressing very high, sometimes we managed to steal the ball very high we had many chances after scoring the first goal.
Then, for different reasons, because of football too, they scored two goals and went ahead.
In the second half, we made some changes. The players who came on from the bench did very well.
We listened to the manager and we improved many things. That worked for us to get the victory.